Author's Comments:In this paper, I study the Finsler structures on the
2-sphere whose
Finsler-Gauss curvature is identically 1. I show that
these structures
can be regarded as more classical geometric
structures on the `dual' 2-sphere
of geodesics of the structure and use this fact to
construct explicit examples
that are not Riemannian.

A longer and more expository version of this article
is available he
re.